1. Field of the Invention
The present invention is directed to a method and apparatus for computed tomography.
2. Description of the Prior Art
A computed tomography method is known wherein, a subject is scanned with a conical ray beam emanating from a focus and with a matrix-like detector array for detecting the ray beam, with the focus being moved on a spiral path around a system axis relative to the subject, and the detector array supplies output data corresponding to the received radiation, and wherein images of an object region executing a periodic motion are reconstructed from output data respectively supplied during the motion of the focus on a spiral segment, the images being reconstructed dependent on the time curve of a signal that is acquired during the scanning that reflects the time curve of the periodic motion.
A computed tomography (CT) apparatus also is known having a radiation source with a focus from which a conical ray beam emanates, a matrix-like detector array for detecting the ray beam, which supplies output data corresponding to the received radiation, means for generating a relative motion between the radiation source/detector array and a subject, on the other hand, and an image computer to which the output data are supplied, wherein the means for producing a relative motion for scanning the subject produce a relative motion of the focus with respect to a system axis such that the focus moves on a helical spiral path relative to the system axis, the middle axis of the spiral path corresponding to the system axis, a device for obtaining a signal during the scanning which represents the time curve of the periodic motion, and an image computer that reconstructs images of an object region executing the periodic motion from the detector output data respectively and the periodic motion signal.
German OS 198 42 238 discloses such a method and apparatus. A disadvantage of this method is that it is suited only for detector arrays having a relatively small extent in the direction of the system axis.
Various CT methods making use of a conical X-ray beam are known, particularly in conjunction with detectors having several lines of detector elements. The cone angle that occurs as a consequence of the conical shape of the X-ray beam is thereby taken into account in different ways.
In the simplest case (see, for example, B. K. Taguchi, H. Aradate, xe2x80x9cAlgorithm for image reconstruction in multi-slice helical CTxe2x80x9d, Med. Phys. 25, pp 550-561, 1998; H. Hu, xe2x80x9cMulti-slice helical CT: Scan and reconstructionxe2x80x9d, Med. Phys. 26, pp. 5-18, 1999), the cone angle is left out of consideration, with the disadvantage that artifacts occur given a large number of detector lines, and thus a large cone angle.
Further, an algorithm referred to as the MFR algorithm (S. Schaller, T. Flohr, P. Steffen, xe2x80x9cNew, efficient Fourier-reconstruction method for approximate image reconstruction in spiral cone-beam CT at small cone-anglesxe2x80x9d, SPIE Medical Imaging Conf., Proc. Vol. 3032, pp. 213-224, 1997) is known. A disadvantage of this method is that a complicated Fourier reconstruction is needed and the image quality leaves something to be desired.
Exact algorithms also have been disclosed (see, for example, S. Schaller, F. Noo, F. Sauer, K. C. Tam, G. Lauritsch, T. Flohr, xe2x80x9cExact Radon rebinning algorithm for the long object problem in helical cone-beam CTxe2x80x9d, in Proc. of the 1999 Int. Meeting on Fully 3D Image Reconstruction, pp. 11-14, 1999 or H. Kudo, F. Noo and M. Defrise, xe2x80x9cCone-beam filtered backprojection algorithm for truncated helical dataxe2x80x9d, in Phys. Med. Biol., 43, pp. 2885-2909, 1998), these having the common disadvantage of an extremely complicated reconstruction.
A method and CT apparatus of the type initially described also are disclosed in U.S. Pat. No. 5,802,134. As disclosed therein, images are reconstructed for image planes that are inclined relative to the system axis z by an inclination angle xcex3 around the x-axis. As a result, the (at least theoretical) advantage is achieved of the images containing fewer artifacts when the inclination angle xcex3 is selected such that a good, optimum adaptation of the image plane to the spiral path is established, insofar as possible according to a suitable error criterion, for example the minimum quadratic average of the distance of all points of the spiral segment from the image plane as measured in the z-direction.
In the case of U.S. Pat. No. 5,802,134, fan dataxe2x80x94i.e. data registered using known fan geometryxe2x80x94that were acquired given the motion of the focus over a spiral segment having the length 180xc2x0 plus fan angle, for example 240xc2x0, are thereby employed for the reconstruction. The optimum inclination angle xcex3 is dependent on the slope of the spiral, and on the pitch p.
The method disclosed in U.S. Pat. No. 5,802,134 can be employed for arbitrary values of the pitch p. An optimum utilization of the available detector area and thus of the radiation dose applied to the patient for image acquisition (detector and, thus, dose utilization), however, is not possible below a maximum pitch pmax. This is because even though a given transverse slice, i.e. a slice of the subject residing at a right angle relative to the system axis z, that is longer than 180xc2x0 plus fan angle is scanned over a spiral segment, only a spiral segment of the length 180xc2x0 plus cone angle can be used for values of the pitch p below the maximum pitch pmax, since the use of a longer spiral segment would make it impossible to adapt the image plane adequately well to the spiral path.
An object of the present invention is to provide a method and a CT apparatus of the type initially described which are also suited, i.e. enable high-quality images, for detector arrays having a large extent in the direction of the system axis.
The above object is achieved in accordance with the invention in a computed tomography method and apparatus wherein a subject having a subject with a conical ray beam emanating from a focus and with a matrix-like detector array for detecting the ray beam, while the focus is moved on a spiral path around a system axis relative to the subject, and the detector array supplies output data corresponding to the received radiation. The output data respectively supplied during the motion of the focus on a spiral segment and having a length adequate for the reconstruction of a CT image are divided into output data with respect to sub-segments, with the length of each sub-segments being shorter than the length required for the reconstruction of a CT image. Segment images having an inclined image plane relative to the system axis are reconstructed for the sub-segments. A signal reproducing the time curve of the periodic motion is acquired during the scanning. A z-position on the system axis and a time position with respect to the periodic motion are allocated to the segment images. Segment images belonging to a desired range of z-positions and a desired range of time positions are selected such that the corresponding sub-segments have an overall length adequate for the reconstruction of a CT image. The selected segment images are at least indirectly combined into a resulting CT image with respect to a target image plane.
In the invention, the cone angle is taken into consideration since sub-segments are first formed and segment images are reconstructed with respect to the sub-segments, the deviations of the image areas from the spiral path along the sub-segments being very small for these segment images since the length of each sub-segment is shorter than the length required for the reconstruction of a CT image. The segment images thus contain only very slight deviations of the image areas of the segment images from the spiral path along the sub-segments, so that the image quality in the generation of the resulting CT image is high even given a large number of detector lines.
Since the segment images have a z-position on the system axis and a time position with respect to the time curve of the periodic motion allocated to them, it is easily possible in the invention to select only those segment images for compilation into a resulting CT image of a desired target image area that lie in a desired range in view of their z-position as well as in view of their time position. It must be assured that the sub-segments belonging to the selected segment images exhibit an overall length that suffices for the reconstruction of a CT image (for example, 180xc2x0 plus fan angle).
Whereas the method disclosed in German OS 198 42 238 is suitable for multi-line detectors having up to a maximum of approximately ten through twelve lines of detector elements (based on a width of a line of detector elements of 1 mm measured in the direction of the system axis), the inventive method (based on the same width of a line of detector elements) supplies high-quality images even given an extremely large number of lines of, for example, sixty four lines.
According to one version of the invention, the selected segment images belong to sub-segments derived from a single phase of the periodic motion, again with the overall length of the sub-segments being sufficient for the reconstruction of a CT image.
Alternatively, the selected segment images can belong to sub-segments derived from a number of phases of the periodic motion, with the overall length of the sub-segments being sufficient for the reconstruction of a CT image. This procedure offers the advantage of a higher time resolution, this being achieved by the use of sub-segments of the same motion phase in successive phases of the periodic motion (for example, heartbeats) for the reconstruction. These sub-segments correspond to a narrower time window.
Fundamentally, there is the possibility of combining the selected segment images directly to form the resulting CT image, this being particularly simple when the target image area corresponds to the z-position of the selected segment images. Insofar as the z-positions of the selected segment images differ from the target image area, the segment images in one version of the invention are reformatted onto the target image area before being combined into the resulting CT image. This can be accomplished, for example, by interpolation.
According to one version of the invention, the selected segment images are directly combined to form the resulting CT image by the selected segment images belonging to a sub-segment being combined into a sub-image (or partial image) with respect to the target image area, before the sub-images are combined into a resulting CT image.
For imaging a volume, in an embodiment of the invention CT images of successive subject slices in the direction of the system axis are generated. The successive subject slices should adjoin one another for producing a gap-free presentation of the volume.
The pre-requisites for an optimum detector, and thus dose utilization, are also established in the invention for values of the pitch p below the maximum pitch pmax. In order to have data available for a gap-free presentation of a volume, however, the maximum pitch pmax cannot be utilized without further measures. The slope of the spiral path must be limited, for example in the way disclosed in German OS 198 42 238, such that the sub-volumes reconstructed in every cycle of the periodic motion fit each other gap-free.
So that the feed is not excessively limited, in a version of the invention the image areas of the segment images are not planar but are curved, for enlarging the volume acquired with the segment images belonging to a sub-segment.
If it should occur that the feed was selected too large, repetition of the examination can be avoided by the missing segment images being calculated by interpolation from segment images from the preceding or following period of the motion, dependent on the desired z-positions and time positions.
The maximum inclination of the image surfaces of the segment images is determined from weighting for the image area of each segment image must be present at both ends of a sub-segment within the measurement field.
The segment images, which are unusable by themselves because of the fact that that the length of each sub-segment is shorter than the length required for the reconstruction of a CT image, are calculated in a known way, i.e. the rays that are most beneficial for the image area of the respective segment image are selected from the projections for the respective sub-segment in parallel or fan geometry according to a suitable error criterion, and are filtered and back-projected, or reconstructed with another standard method.
A useable image arises only given the direct or indirect combination o the selected segment images to form a resulting CT image, i.e. given reformatting onto the target image area.
The image quality of this image is especially high when the segment images are reconstructed for image planes that are inclined around a first axis intersecting the system axis at a right angle by an inclination angle "khgr" as well as around a second axis intersecting each of the first and the system axis at a right angle by a tilt angle xcex4 with respect to the system axis because the adaptation of the image planes of the segment to the spiral path of the respective sub-segment is then better again.
In an embodiment of the invention, the neighboring sub-segments overlap, so the output data belonging to the overlap regions are respectively weighted such that the weights of output data corresponding to one another in the overlapping sub-segments produce a value of one.
The advantage of overlapping sub-segments is that artifacts that would otherwise occur at the adjoining edges of the sub-segments are avoided.
In an embodiment, segment images for a number nima of inclined image planes are reconstructed for each sub-segment, whereby the image planes have different z-positions zima. Due to the reconstruction of a number of segment images having differently inclined image plane for different z-positions, it is possiblexe2x80x94by a suitable selection of the inclination angle xcex3 and of the tilt angle xcex94xe2x80x94to optimally adapt the image plane of the respective segment image for each of these z-positions to the sub-segment and to thus utilize the detector array as well as the dose completely in theoretical terms and to the greatest extent in practice. In a preferred embodiment of the invention, the number of inclined image planes intersect in a straight line that proceeds tangentially relative to the sub-segment.
In order to obtain an optimally complete detector utilization and dose utilization, the following applies according to a version of the invention for the extreme values +xcex4max and xe2x88x92xcex4max of the tilt angle xcex4 of the inclined image planes belonging to a sub-segment:       ±          δ      max        =      arctan    ⁢          (                                    bM            2                    +                                    Sp              ⁢                              xe2x80x83                            ⁢                                                α                  1                                                  2                  ⁢                  π                                                      ±                          RFOV              ⁢                              xe2x80x83                            ⁢              cos              ⁢                              xe2x80x83                            ⁢                              α                1                            ⁢              tan              ⁢                              xe2x80x83                            ⁢                              γ                0                                                                          -                                          R                f                                            cos                ⁢                                  xe2x80x83                                ⁢                                  γ                  0                                                              -                                    (                              ±                RFOV                            )                        ⁢                                          sin                ⁢                                  xe2x80x83                                ⁢                                  α                  1                                                            cos                ⁢                                  xe2x80x83                                ⁢                                  γ                  0                                                                        )      
wherein xcex30 is the value of the inclination angle xcex3 determined for the tilt angle xcex4=0 according to       γ          0      =      tan        ⁢      (                            -          Sp                ⁢                  xe2x80x83                ⁢                  α          ^                            2        ⁢                  xe2x80x83                ⁢        π        ⁢                  xe2x80x83                ⁢                  R          f                ⁢        sin        ⁢                  xe2x80x83                ⁢        α              )  
and b is the width of a detector line and S is the length of the spiral path.
For a high image quality, in another version of the invention the optimum value xcex3min of the inclination angle belonging to a given amount |xcex4max| of the maximum value of the tilt angle xcex4 is determined such that an error criterion is met, for example minimum average of the squares the respective spacings of all points of the sub-segment from the image plane measured in the z-direction, is met.
If the rotational axis, around which the focus rotates around the system axis, is not identical with the system axis but intersects the system axis at an angle referred to as a gantry angle xcfx81, then the following applies to the inclination angle xcex3xe2x80x2 to be selected:       γ    xe2x80x2    =      arctan    ⁢          xe2x80x83        ⁢                            Sp          ·          cos                ⁢                  xe2x80x83                ⁢        ρ                                          4            ⁢                                          π                2                            ·                              R                f                                              +                                    S              2                        ⁢                          P              2                                +                      4            ⁢                          π              ·                              R                f                                      ⁢                          xe2x80x83                        ⁢            cos            ⁢                          xe2x80x83                        ⁢            α            ⁢                          xe2x80x83                        ⁢            sin            ⁢                          xe2x80x83                        ⁢                          ρ              ·              Sp                                          
Here, as well, there is the possibility of determining the appertaining optimum value of the inclination angle xcex3xe2x80x2 for a given magnitude of the maximum value of the tilt angle |xcex4max| such that an error criterion, for example minimum average of the squares of the respective spacings of all points of the sub-segment from the image plane measured in the z-direction.
In order to obtain an optimally complete detector and dose utilization, the following is also valid according to a version of the invention for the number nima of the inclined image planes, for which segment images with inclined plane are generated for each sub-segment:       n    ima    =      floor    ⁢          xe2x80x83        [          sM      p        ]  
wherein s is the length of the sub-segments.
Likewise for an optimally complete detector and dose utilization, the tilt angles xcex4 of the inclined image planes are determined in a version of the invention according to       δ    ⁢          (      i      )        =            δ      max        ⁢                            2          ⁢          i                -                  (                                    n              ima                        -            1                    )                                      n          ima                -        1            
given the condition of detector lines of equal width.
In order to create the conditions for obtaining transverse tomograms to which the users of CT apparatus are accustomed, a reformatting is provided according to one version of the invention, i.e. a sub-image is generated in a further method wherein a number of segment images are combined. In an embodiment of the invention, it may occur that a number of segment images are combined to form a sub-image by interpolation or by, in particular, weighted averaging.
The reconstruction slice thickness of the sub-images, and thus of the resulting CT image is set according to a preferred embodiment of the invention by weighting the segment images according to the desired reconstruction slice thickness of the sub-image in the combining to form a sub-image.
In a version of the invention the compression is reversed during the course of the combining of the segment images belonging to a sub-segment to form a sub-image exhibiting a uniform pixel matrix. Compared to reversing the compression only during the course of the combining of the sub-images to form the resulting CT image, this offers the advantage of an enhanced image quality. In view of this advantage, compared whereto the somewhat larger quantity of data due to the employment of uncompressed sub-images is negligible.
According to versions of the invention, the pixels of the uniform pixel matrix of a sub-image are acquired by interpolation or by averaging from the pixels of the non-uniform pixel matrix of the segment images when combining the segment images belonging to a sub-segment to form a sub-image.
The above object also is achieved in a computed tomography apparatus operating according to the inventive CT method described above. The comments and discussion above relating to the inventive CT method apply equally to the inventive CT apparatus.